The title is proper grammar. The letter i represents the imaginary number and creates complex numbers.

I have a problem with paradox and sqrt(-1) and a few other things that I ( not imaginary ) cannot accept as elements of a rational mathematical system. The picture resolves the difference between how I view multiplication. Imaginary numbers arose in the solutions of a equations. They are applied in electronics and physics. I understand the numbers differently. There are numbers that apply to quantity and those that apply to dimensional space. In quantities, I can have 10 fewer of some object and that is not illogical. It is the presumption that a number system is consistent in its rules across many applications. In some cases x·y is not the same as x×y or y·x

You might think that I reject things like eiπ as bad math. That is not the case. It is the fact that mathematics has failed to be flexible enough to correct its own structure. Numbers were once considered to have mystical powers. I see the computations in a very straight forward and consistent way and this i is a symptom of the vision of Alice Through the Looking Glass. A mixed metaphor of calculation. It unnecessarily complicates the application and understanding of physical systems. Math is method. It is the same as programming in almost all aspects. In this case there are procedures that depend on the order of their execution and it is not explicit in the design of the number system.

When someone is contemplating i2, they are contemplating the resolution of a paradox created in the specification of the system of calculus itself.

It is quite clear that dimensionality and order are applied in vectors like <i,j,k> and the methods which act upon them are correct, however, the whole of the system of mathematical modelling is inconsistent in its association of methods to objects. In object oriented programming the same method is used for like objects. When a method is applied to an object of different properties an anomaly occurs and though the anomaly may be resolved in the application, it still is improperly implemented. If one procedure adds 1 to all letters and they are displayed by subtracting 1 when they originate from an improper method, then the result is the same, but the process is unnecessarily convolute and becomes difficult to express and teach. It is like a box with negative width, depth, and height. The traverse of negative space is very much different. I consider that multiplication is not commutative in some cases. I also presume that -1 &times -1 sometimes implies the addition of an operator which is -|- . It was a long time before zero was admitted into the lexicon and method of calculus. It can be 00 ( zero to the zeroth power = 1, or one) messy problem when the system of logic itself is inconsistent.